Question

In the given figure abcd and aefg are Two parallelograms prove that area of abcd is equal to area of aefg

Answer 1

If ABCD and AEFG lie on same base and btw same parallels then are equeal in area

Answer 2

Parallelograms on same base and same parallel lines are equal in area

Step-by-step explanation:

Construction - Join BG

Parallelogram AEFG and ΔABG lie on same base AG & between parallel lines AG & EF.

So,

ar ΔABG = $\frac {1}{2}$(ar AEFG) ""(1)

Parallelogram ABCD and ΔABG lie on same base line AB & between same parallel lines AB & CD

So,

ar ΔABG = $\frac {1}{2}$ (ar ABCD) ""(2)

From equations (1) & (2) -

ar AEFG = ar ABCD

This Proves that Parallelograms on same base and same parallel lines are equal in area